Problem: Rewrite as a simplified fraction. ${1.2\overline{25} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1225.2525...\\ 10x &= 12.2525...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1213}$ ${x = \dfrac{1213}{990}} \text{or} {1 \dfrac{223}{990}}$